Blast Design Formulas [PDF]

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THE BLASTER’S GUIDE

COMMON FORMULAS USED FOR BLAST DESIGN

BLAST DESIGN FORMULAS Absolute Bulk Strength (ABS) .................................................................................... Absolute Weight Strength (AWS) ................................................................................ Actual Scaled Distance ............................................................................................ Base-Charge Length ............................................................................................... Burden .................................................................................................................. Deck Stemming ......................................................................................................

8 8 8 8 9 9

-For Dry Holes -For Wet Holes

Face Height ........................................................................................................... 9 Hole-to-Hole Delay Time .......................................................................................... 9 Loading Density .................................................................................................... 10 Maximum Charge Weight per Delay .......................................................................... 10 Minimum Distance.................................................................................................. 10 Powder Factor ...................................................................................................... 10 -Volume of Rock Input -Weight of Rock Input

Pre-Splitting Formulas for Air-Decked Charges .......................................................... 11 -Spacing of Air-Decked Charges -Weight of Air-Decked Charges -Stemming Column Length

Pre-Splitting Formulas for De-Coupled Charges ......................................................... 11 -Linear Charge Weight -Spacing between Pre-Split Holes

Pressure Formula .................................................................................................. 11 Relative Weight Strength (RWS) ............................................................................... 12 Resistance Formulas ............................................................................................. 12 -For Paralle Circuits -For Series Circuits

Row-to-Row Delay Time ......................................................................................... 12 Stone Stemming Particle Size .................................................................................. 12 Spacing ............................................................................................................... 13 -Instant -Delayed

Sub-Drilling .......................................................................................................... “Supersonic” Face Velocity ..................................................................................... Top-Stemming Length ........................................................................................... Water Displacement .............................................................................................. Weight of Rock per Blast Hole ................................................................................. Vibration Level Prediction .......................................................................................

13 13 13 14 14 14

-Peak Particle Velocity Prediction -Site Specific Ground Transmission Constant

Volume of Rock per Blast Hole ................................................................................ 14

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THE BLASTER’S GUIDE

BLAST DESIGN FORMULAS HOW TO READ FORMULAS

FORMULA NAME

FORMULA VARIABLES and [UNITS]

Variables used in formula and required units in [brackets]. If input variables are not in required units, then you must use the unit conversion tables.

Absolute Bulk Strength (ABS)

ABS E � AWSE � dE

Base-Charge Length Formula

Eb �

�� 0.3

VARIABLES and [UNITS]

E b = Length of base charge of high density explosives [ft] B = Average burden [ft] J = Sub-drilling depth [ft]

Acutual Scaled Distance Formula

Actual Scaled Distance

VARIABLES and [UNITS]

ABS E = Absolute bulk strength of the explosive [cal/cc] AWS E = Absolute weight strength of the explosive [cal/g] d E = Density of the explosive [g/cm 3 ]

SD �

RBS E � 7 . 462

AWS E = Absolute weight strength of the explosive [cal/g] RBS E = Relative bulk strength of the explosive [ANFO = 100] d E = Density of the explosive [g/cm 3 ] © 2 0 0 2 AU S T I N PO W DE R C O M P AN Y

W

� D � W �� � � SD �

2

Minimum Distance

D � SD �

dE

VARIABLES and [UNITS]

D

Maximum Charge Weight per Delay

Absolute Weight Strength (AWS)

AWS E �

� 0.5 � � B � � J

W

VARIABLES and [UNITS]

SD = Scaled distance factor W = Charge weight per delay [ lb ] D = Distance [ft]

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THE BLASTER’S GUIDE

BLAST DESIGN FORMULAS

Burden Formula Hole-to-Hole Delay Time Formula � � �d � B � De � ��2 � � e � � 1.5�� � � dr � �

D hth � � 0 � 5 � � S ms/ft

VARIABLES and [UNITS]

B = Burden [ft] de = Density of the explosives [g/cm 3 ] dr = Density of the rock [g/cm 3 ] De = Diameter of fully coupled explosive column [in]

VARIABLES and [UNITS]

Dhth = Delay time between holes in a row [ms] S = Spacing between holes in a row [ft]

Hole-to-Hole Delay Times to Improve Fragmentation

Deck Stemming Formula

For Dry Holes

Td � 0.5 � D

For Wet Holes

Td � 1.0 � D

VARIABLES and [UNITS]

Rock Type

ms/ft

Sands, Loams, Marls and Coals

1.8 - 2.1

Some Limestones, Rock Shale and some Shales

1.5 - 1.8

Compact Limestones and Marbles, some Granites and Basalts, Quartzite Rocks and some Gneisses and Gabbros

1.2 - 1.5

Diabase, Diabase Porphyrites, Compact Gneisses, and Mica Schists and Magnetites

0.9 - 1.2

Td = Minimum length of stone deck consisting of particles of size Ts [ft] D = Blast-hole diameter [in]

Face Height Formula

H�

5

10 � D

VARIABLES and [UNITS]

H = Face Height [ft]

Leading underground mining technology.

D = Blast-hole Diameter [in]

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THE BLASTER’S GUIDE

BLAST DESIGN FORMULAS

Loading Density Formula

2

d l � 0.3404 � De � d e

Minimum Distance Formula

D � SD �

W

VARIABLES and [UNITS]

VARIABLES and [UNITS]

d l = Explosives loading density [lb /ft] De = Diameter of explosives column [in] de = Density of explosives [g/cm 3 ]

SD = Scaled distance factor W = Charge weight per delay [lb] D = Distance [ft]

Powder Factor Formula Volume of Rock

PF �

We V

VARIABLES and [UNITS]

Loading a blast on an iron ore range.

PF = Powder factor [lb/yd 3 ] We = Total weight of explosives used in blast [lb] V = Total volume of rock generated in blast [yd3 ]

Maximum Charge Weight per Delay

� D � � � SD �

Weight of Rock

PF �

2

W �� VARIABLES and [UNITS]

SD = Scaled distance factor W = Charge weight per delay [ lb] D = Distance [ft]

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Wr We

VARIABLES and [UNITS]

PF = Powder factor [t/lb] Wr = Total weight of rock generated in blast [t] We = Total weight of explosives used in blast [lb]

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THE BLASTER’S GUIDE

BLAST DESIGN FORMULAS

Pre-Splitting Formulas for Air-Decked Charges

Pre-Splitting Formulas for De-Coupled Charges Linear Charge Weight

Spacing of Air-Decked Charges

S

2

D Wl � 28

� �1 .5 � 2 .0 � � D VARIABLES and [UNITS]

VARIABLES and [UNITS]

S = Spacing between air-decked holes [ft] D = Diameter of blast-hole [in]

Wl = Linear charge weight for pre-splitting explosive [lb/ft] D = Diameter of blast-hole [in]

Spacing between Pre-Split Holes Weight of Air-Decked Charges

W

S�

� �0 .08 � 0 .12 � � S � Lh

D

2

2.8

VARIABLES and [UNITS] VARIABLES and [UNITS]

S = Spacing between pre-split holes [ft] D = Diameter of blast-hole [in]

W = Weight of air-deck charge [lb] S = Spacing between blast-holes [ft] Lh = Length of blast-hole [ft]

Pressure Formula Stemming Column Length

T � �1 .0 � 1 .2 � � D VARIABLES and [UNITS]

T = Stemming column length [ft] D = Diameter of blast-hole [in]

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2

P � 0.000000233 � VOD � d E VARIABLES and [UNITS]

P = Pressure [kbar] VOD = Velocity of detonation of explosive [ft/sec] d E = Density of explosive [g/cm 3 ]

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THE BLASTER’S GUIDE

BLAST DESIGN FORMULAS

Relative Weight Strength (RWS) Row-to-Row Delay Time Formula RWS E �

AWS E 91,000

Drtr � � 2 � 15 � � B ms/ft

VARIABLES and [UNITS]

RWS E = Relative weight strength of the explosive [ANFO = 100] AWS E = Absolute weight strength of the explosive [cal/g]

VARIABLES and [UNITS]

D rtr = Delay time between consecutive rows [ms] B = Maximum burden in front of a row of holes [ft]

Effects of Various Row-to-Row Delays

Resistance Formulas

For Parallel Circuits 1 1 1 1 1 � � � � ... � Rtotal R1 R2 R3 Rn

Effects

ms/ft

Violent excessive air-blast and back-break

2

High pile close to face, moderate air-blast and back-break

2-3

Average pile height, average air-blast and back-break

3-4

Scattered pile with minimum back-break

4-6

For Series Circuits Rtotal � R1 � R2 � R3 � ... � Rn

Stone Stemming Particle Size Formula

VARIABLES and [UNITS]

Rtotal = Total resistance of the electrical circuit [ �] R1 ... R n = Resistance of individual blasting caps or circuit branches [ �]

Ts �

D 12 � 20

VARIABLES and [UNITS]

T s = Clean crushed stone stemming particle size [in] D = Blast-hole diameter [in]

Bulk trucks preparing for another day on the job. © 2 0 0 2 AU S T I N PO W DE R C O M P AN Y

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THE BLASTER’S GUIDE

BLAST DESIGN FORMULAS

Sub-Drilling Formula Spacing Formulas J � � 0.2 � 0.5 � � B If: VARIABLES and [UNITS]

B = Burden [ft] J = Sub-drilling [ft]

H �4 B

If:

Instant

S � 2.0 � B

S�

Delayed

S � 1.4 � B

S�

H